Prepared By TJS ENGINEERING COLLEGE STUDENTSDijkstras AlgorithmAim:Given a graph with appropriate weights for each node, find the single source shortest path using Dijkstras algorithm.

Algorithm:algorithm DijkstraShortestWeightedPath(G, s)_ pre-cond_: G is a weighted (directed or undirected) graph, and s is one of its nodes._ post-cond_: specifies a shortest weighted path from s to each node of G, and d specifiestheir lengths.begind(s) = 0, (s) = _for other v, d(v)=and (v) = nilhandled = notHandled = priority queue containing all nodes. Priorities given by d(v).loop_loop-invariant_: See above.exit when notHandled = let u be a node fromnotHandled with smallest d(u)for each v connected to ufoundPathLength = d(u) +w_u,v_if d(v) > foundPathLength thend(v) = foundPathLength(v) = u(update the notHandled priority queue)end ifend formove u from notHandled to handledend loopreturn _d, _end algorithm

SOURCE CODE: package dijkstrashortestpath;import java.util.InputMismatchException;import java.util.Scanner; public class DijkstraShortestPath{ private boolean settled[]; private boolean unsettled[]; private int distances[]; private int adjacencymatrix[][]; private int numberofvertices; public DijkstraShortestPath(int numberofvertices) { this.numberofvertices = numberofvertices; this.settled = new boolean[numberofvertices + 1]; this.unsettled = new boolean[numberofvertices + 1]; this.distances = new int[numberofvertices + 1]; this.adjacencymatrix = new int[numberofvertices + 1][numberofvertices + 1]; } public void dijkstraShortestPath(int source, int adjacencymatrix[][]) { int evaluationnode; for (int vertex = 1; vertex = maze.length || square.y < 0 || square.y >= maze[square.x].length ) {

return false; }

return ( maze[square.x][square.y] == FREE_CHAR || maze[square.x][square.y] == FINISH_CHAR ); } private void enterSquare ( Point square ) { maze[square.x][square.y] = PATH_CHAR; totalSteps++; }

private void exitSquare ( Point square ) { maze[square.x][square.y] = FREE_CHAR; totalSteps--; } private boolean mazeFinished ( Point location ) { return location.equals(finishLocation); }

public void printMaze() { for ( int i = 0; i < maze.length; i++ ) { for ( int j = 0; j < maze[i].length; j++ ) { System.out.print(maze[i][j]); } System.out.println(); } System.out.println(); }

private Point getStartLocation() { Point startLocation = findChar(START_CHAR); if ( startLocation == null ) { throw new IllegalStateException("Maze has no start square!"); }

return startLocation; }

private Point getFinishLocation() { Point finishLocation = findChar(FINISH_CHAR); if ( finishLocation == null ) { throw new IllegalStateException("Maze has no finish square!"); }

return finishLocation; }

private Point findChar( char c ) { for ( int i = 0; i < maze.length; i++ ) { for ( int j = 0; j < maze[i].length; j++ ) { if ( maze[i][j] == c ) { return new Point(i, j); } } } return null; } public static void main ( String[] args ) { char[][] easyMaze = { { WALL_CHAR, START_CHAR, WALL_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR }, { WALL_CHAR, FREE_CHAR, WALL_CHAR, WALL_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, WALL_CHAR }, { WALL_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR }, { WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR }, { WALL_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR }, { WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, WALL_CHAR }, { WALL_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, FREE_CHAR, FREE_CHAR, WALL_CHAR, FREE_CHAR, FINISH_CHAR }, { WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR, WALL_CHAR } };

MazeSolver s = new MazeSolver(easyMaze); System.out.println("The maze looks like:"); s.printMaze();

s.solve(); }}

OUTPUT:

RESULT:

For a given maze of size 12*12, the program successfully computed the path from source the destination

GRAPH COLORING USING BACKTRACKINGAim:Given a graph, to color using backtracking in java

Algorithm:Given G=(V,E):Compute Degree(v) for all v in V.Set uncolored = V sorted in decreasing order of Degree(v).set currentColor = 0.while there are uncolored nodes:set A=first element of uncoloredremove A from uncoloredset Color(A) = currentColorset coloredWithCurrent = {A}for each v in uncolored:if v is not adjacent to anything in coloredWithCurrent:set Color(v)=currentColor.add v to currentColor.remove v from uncolored.end ifend forcurrentColor = currentColor + 1.end while

SOURCE CODE: import java.io.*;public class GraphColoring{static int [][] G;static int [] x;static int n, m;static boolean found = false;public static BufferedReader br =new BufferedReader(new InputStreamReader(System.in));public static void main(String[] args) throws IOException{System.out.println("\t\t\t\tGRAPH COLORING");System.out.print("\nEnter the number of the vertices: ");n = Integer.parseInt(br.readLine());G = new int[n+1][n+1];x = new int[n+1];System.out.print("\nIf edge between the following vertices enter 1 else 0:\n");for(int i=1;i